Average-Price and Reachability-Price Games on Hybrid Automata with Strong Resets

We introduce and study hybrid automata with strong resets. They generalize o-minimal hybrid automata, a class of hybrid automata which allows modeling of complex continuous dynamics. A number of analysis problems, such as reachability testing and controller synthesis, are decidable for classes of ominimal hybrid automata. We generalize existing decidability results for controller synthesis on hybrid automata and we establish new ones by proving that average-price and reachability-price games on hybrid systems with strong resets are decidable, provided that the structure on which the hybrid automaton is defined has a decidable first-order theory. Our proof techniques include a novel characterization of values in games on hybrid systems by optimality equations, and a definition of a new finitary equivalence relation on the states of a hybrid system which enables a reduction of games on hybrid systems to games on finite graphs.